Radio-wave arrival-direction estimating apparatus and directional variable transceiver

ABSTRACT

A radio-wave arrival-direction apparatus calculates a correlation matrix of received signals by correlation calculation between antenna elements, and calculates a noise spatial eigenmatrix, of which each row or column is an eigenvector belonging to a noise eigen-space, by eigenvalue factorization of the correlation matrix. The apparatus also factorizes a matrix including a product of the noise spatial eigenmatrix and a conjugated and transposed matrix of it to an upper or lower triangular matrix, using cholesky factorization. The apparatus calculates an angle evaluation value in a predetermined angle range of an arrival-angle evaluation function using the derived upper or lower triangular matrix, and determines an arrival angle based on the calculation result. A calculation amount in a variable angle range can be thus reduced without causing accuracy degradation of arrival direction, in an algorism requiring an angle sweep for arrival angle estimation of MUSIC method or the like.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 10/020,477, filed Dec. 12, 2001, now U.S. Pat. No. 6,642,888.

FIELD OF THE INVENTION

The present invention relates to a radio-wave arrival-directionestimating apparatus employing an array antenna, and a directivityvariable transceiver for varying antenna directivity based on anestimation result from the estimating apparatus.

BACKGROUND OF THE INVENTION

An arrival direction of radio wave is conventionally estimatedaccurately in a method such as Multiple Signal Classification (MUSIC)method, using an array antenna comprising a plurality of antennaelements. The MUSIC method is disposed in R. O. Schmidt, “MultipleEmitter Location and Signal Parameter Estimation”, Institute ofElectrical and Electronics Engineers (IEEE) Trans., AP-34, pp. 276-280(1986). This method includes an algorism for accurately estimating adirection of a plurality of incident waves with the same frequency band.

In this method, M (>1) antenna elements receive signals, and a receivingunit connected to each antenna element converts the frequency of each ofthe received signals, detects a phase of it, and demodulates thereceived signal to a signal comprising orthogonal I and Q signals. Ananalog/digital converter (A/D converter) converts the demodulated signalto sampling data and outputs the data to a direction estimatingprocessor. The direction estimating processor estimates a direction ofthe incident waves using the sampling data by the MUSIC method. In otherwords, using sampling data x₁ (k), x₂ (k), . . . , x_(M) (k) at samplingtime kΔT obtained by respective antenna elements, a correlation matrixcalculation unit creates receiving vector x (k) written as

x(k)=[x ₁(k)x ₂(k). . . x _(M)(k)]^(r)  (Equation 1),

where T shows transposition of a vector, ΔT is a sampling interval, andk is a natural number. The correlation matrix calculation unit, usingreceiving vectors x (k) for k=1 to N, further finds M×M correlationmatrix R written as $\begin{matrix}{R = {\sum\limits_{k = 1}^{N}{{x(k)}{{x(k)}^{H}/N}}}} & {\left( {{Equation}\quad 2} \right),}\end{matrix}$

where H shows complex conjugate transposition of a vector.

The calculation unit calculates eigenvalues λ₁-λ_(M) of correlationmatrix R in the descending order, and eigenvactors e₁-e_(M)corresponding to eigenvalues λ₁-λ_(M).

Next, the calculation unit calculates an evaluation value of anarrival-angle evaluation function, assuming number of the incident wavesis S, and using noise spatial eigenmatrix E_(N)=[e_(S+1), . . . , e_(M)]and a feature that signal eigenvector space E_(S)=[e₁, . . . , e_(S)]and E_(N) are orthogonal to each other. This E_(N) is formed with (M−S)eigenvactors, namely column vectors, belonging to a noise eigenvactorspace having the relation written as

λ₁≧λ₂≧. . . ≧λ_(s)>λ_(s+1)=λ_(s+2)=. . . =λ_(M)  (Equation 3),

and E_(S) is formed with eigenvactors e₁-e_(S). In other words,arrival-angle evaluation function F(θ) for evaluating orthogonalitybetween E_(N) and E_(S) is defined by $\begin{matrix}{{F(\theta)} = \frac{1}{{a^{H}(\theta)}E_{N}E_{N}^{H}{a(\theta)}}} & {\left( {{Equation}\quad 4} \right),}\end{matrix}$

where a(θ) is a complex response (hereinafter called a steering, vector)of the array antenna as a function of azimuth θ. Azimuth θ varies in apredetermined angle range. When azimuth θ equals to the arrival angle,ideally, arrival-angle evaluation function F(θ) is infinite. A resultantpeak direction of F(θ) from calculation for the varied θ is set to bethe arrival-angle evaluation value of the incident waves.

Number S of incident waves is generally unknown, so that the number isdetermined based on an eigenvalue distribution and number-of-signaldetermination criteria. The criteria is described in M. Wax and T.Kailath, “Detection of Signals by Information Theoretic Criteria”, IEEETrans. On Acoustics, Speech and Signal Processing, Vol. ASSP 33 (2), pp.387-392, February (1985).

The radio-wave arrival-direction estimating apparatus employing theMUSIC method discussed above estimates an arrival direction accuratelyby signal processing, using an algorithm of deriving engenvalue of acorrelation matrix of array received signals. In such an estimatingapparatus, correlation between waves generated by reflection on theground or a building increases when a relative delay time between thesewaves is shorter than a symbol length. In this case, correlation matrixR degrades, and therefore the incident waves cannot be preciselyseparated.

For preventing the degradation, a spatial smoothing technique isproposed. This spatial smoothing technique is described in Pillai et al,“Forward/Backward Spatial Smoothing Techniques for Coherent SignalIdentification”, IEEE Trans. On Acoustics, Speech and Signal Processing,Vol. 37, No. 1, 1989. The example has estimated the arrival directionusing spatial samples from the array antenna; however the MUSIC methodcan be similarly applied to a signal sampled every frequency and thedelay time of the received waves can be estimated at high resolution.

The estimation accuracy of the arrival direction in the MUSIC methoddepends on variation step Δθ of θ in the arrival-angle evaluationfunction (Eq.4). When Δθ increases, a calculation amount in the entirevariation range of θ decreases, but the peak direction of thearrival-angle evaluation function cannot accurately detect the peakdirection and the accuracy decreases. When Δθ decreases, the peakdirection of the arrival-angle evaluation function can be accuratelydetected, but a calculation amount in the entire variation range of θincreases.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a radio-wavearrival-direction estimating apparatus allowing reduction of a totalcalculation amount for an arrival-angle evaluation function withoutcausing accuracy degradation of the arrival direction. It is anotherobject of the present invention to provide a directivity variabletransceiver for improving transmitting and receiving quality bycontrolling antenna directivity.

In the present invention, product of a noise spatial eigenmatrix and aconjugated and transposed matrix of it is a product of an upper or lowertriangular matrix. Therefore, the calculation amount for thearrival-angle evaluation function can be reduced in the entire anglerange for the estimation of the arrival direction. The arrival angleevaluation using the arrival-angle evaluation function that has a heavycalculation load can be significantly reduced during angle sweeping inthe MUSIC method. Processing of the arrival-direction estimatingapparatus can be speeded or an apparatus structure can be simplified.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a radio-wave arrival-direction estimatingapparatus in accordance with exemplary embodiment 1 of the presentinvention.

FIG. 2 is a graph illustrating reduction of a calculation amount inaccordance with exemplary embodiment 1.

FIG. 3 is a graph illustrating a calculation amount required forcholesky factorization in accordance with exemplary embodiment 1.

FIG. 4 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 2 of the present invention.

FIG. 5 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 3 of the present invention.

FIG. 6 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 4 of the present invention.

FIG. 7 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 5 of the present invention.

FIG. 8 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 6 of the present invention.

FIG. 9 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 7 of the present invention.

FIG. 10 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 8 of the present invention.

FIG. 11 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 9 of the present invention.

FIG. 12 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 10 of the present invention.

FIG. 13 is a block diagram of a direction estimating processor inaccordance with exemplary embodiment 11 of the present invention.

FIG. 14 is a graph illustrating an operation of a direction estimatingprocess in accordance with exemplary embodiment 11.

FIG. 15 is a block diagram of a directivity variable receiver inaccordance with exemplary embodiment 12 of the present invention.

FIG. 16 is a block diagram of a directivity variable transceiver inaccordance with exemplary embodiment 12.

FIG. 17 is a block diagram of a directivity variable receiver inaccordance with exemplary embodiment 13 of the present invention.

FIG. 18 is a block diagram of a directivity variable transmitter inaccordance with exemplary embodiment 14 of the present invention.

DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Exemplary embodiments of the present invention are demonstratedhereinafter with reference to the accompanying drawings.

1. First Exemplary Embodiment

FIG. 1 is a block diagram of a radio-wave arrival-direction estimatingapparatus in accordance with exemplary embodiment 1 of the presentinvention. Array antenna 1 comprises M (>1) antenna elements 1—1 to 1-M.Antenna elements 1—1 to 1-M receive high frequency signals 2-1 to 2-M.Receiving units 3-1 to 3-M connected to antenna elements 1—1 to 1-Mconvert frequency of the signals and demodulate the converted signals tosignals 4-1 to 4-M comprising orthogonal I signal and Q signal. A/Dconverters 5-1 to 5-M sample respective I signals and Q signals of thedemodulated signals 4-1 to 4-M, and convert the demodulated signals tocomplex digital signals 6-1 to 6-M. Each of the complex digital signalshas the I signal in its real part and the Q signal in its imaginarypart.

Correlation matrix calculation unit 7 creates receiving vector x (k)given by Eq.1, using complex digital signals x₁ (k), x₂ (k), . . . ,x_(M) (k) at sampling time kΔT derived from complex digital signals 6-1to 6-M. Here k is a natural number and ΔT is a sampling interval.Correlation matrix calculation unit 7 further derives M×M correlationmatrix R written by Eq.2 using receiving vectors x (k) accumulated for Nsampling periods.

Noise spatial eigenmatrix calculation unit 8 applies eigenvaluefactorization to derived correlation matrix R to derive eigenvaluesλ₁-λ_(M) in the descending order and eigenvactors e₁-e_(M) correspondingto them. When a number of the incident waves is S, calculation unit 8outputs noise spatial eigenmatrix E_(N)=[e_(S+1), . . . , e_(M)]comprising (M−S) eigenvactors, namely column vectors, belonging to anoise partial space having the relation given by Eq.3.

Triangular matrix calculation unit 9 derives product U of a noisespatial eigenmatrix and a conjugated and transposed matrix of it as in,

U=E_(N) E_(N) ^(H)  (Equation 5).

Because matrix U is an M×M positive definite matrix, triangular matrixcalculation unit 9, using cholesky factorization, derives lowertriangular matrix L written as

U=L L^(H)  (Equation 6).

Arrival-angle evaluation unit 10 evaluates an arrival angle everypredetermined angle step Δθ using the evaluation function$\begin{matrix}\begin{matrix}{{F_{2}(\theta)} = \frac{1}{{a^{H}(\theta)}L\quad L^{H}{a(\theta)}}} \\{= \frac{1}{{\quad {L^{H}{a(\theta)}}}^{2}}}\end{matrix} & {\left( {{Equation}\quad 7} \right),}\end{matrix}$

where, ∥x∥ is the norm of vector x, and a(θ) is a normalized steeringvector of the array antenna. This evaluation function (Eq.7) is derivedfrom the arrival-angle evaluation function written as Eq.4 using lowertriangular matrix L. Since elements outside the lower triangular part inlower triangular matrix L are null, a ratio of a sum-of-productcalculation amount for the arrival-angle evaluation function given byEq.7 to that in Eq.4 is (M+3)/[2(M−S+1)]. The calculation amount for thefunction given by Eq.7 can be therefore reduced if number S of incidentwaves satisfies S<(M−1)/2.

Referring now to FIG. 2 there is shown a ratio of the calculation amountfor the arrival-angle evaluation function given by Eq.7 to that by Eq.4when number S is 1. FIG. 2 shows that a reduced calculation amount inEq.7 in this method increases as the number of antenna elementsincreases. For example, when the number of antenna elements is 6, thecalculation amount is about 75% of that in the prior art.

Referring now to FIG. 3 there is shown a ratio of the calculation amountfor the cholesky factorization to the calculation amount forarrival-angle evaluation function F(θ_(i)) for one arrival angle θ_(i)in Eq.4 . FIG. 3 shows that the calculation amount for the choleskyfactorization does not reach the calculation amount for arrival-angleevaluation function for five arrival angles even if the number ofantenna elements is 20. The arrival angle evaluation is usuallyperformed for more than 5 arrival angles, so that the increase of thecalculation amount for the cholesky factorization can be consideredextremely smaller than that for the arrival angle evaluation in theentire range of the angle sweep in Eq.7.

Arrival-angle determination unit 11 detects a peak direction based on anarrival-angle evaluation result every Δθ in a variable range of θ, anduses the detected direction as an arrival-angle estimation value of theincident waves.

In the present embodiment, triangular matrix calculation unit 9 appliesthe cholesky factorization to product U of the noise spatial eigenmatrixand the conjugated and transposed matrix of it to derive lowertriangular matrix L. Arrival-angle evaluation function F₂(θ) is derivedby equivalent conversion of the arrival-angle evaluation functionwritten as Eq.4 using matrix L. Additionally, using function F₂(θ), thecalculation amount for the arrival angle evaluation can be reduced underthe condition S<(M−1)/2.

The direction estimation using the MUSIC method has been discussedabove. However, the method of the present embodiment can be as-isapplied to a received signal sampled every frequency when the delay timeof the received wave is estimated at high resolution. That is because anevaluation function similar to that in Eq.4 is used.

The lower triangular matrix is derived by the cholesky factorization inEq.6; however, an upper triangular matrix also obviously produces asimilar advantage.

Triangular matrix calculation unit 9, using a modified choleskyfactorization, may find lower triangular matrix L and diagonal matrix Dexpressed as

U=L D L^(H)  (Equation 8).

The modified cholesky factorization does not require the square rootcalculation, so that calculation time can be reduced.

In this case, arrival-angle evaluation function F₂(θ) is expressed as$\begin{matrix}{{F_{2}(\theta)} = \frac{1}{\sum\limits_{k = 1}^{M}\quad \frac{b_{k}^{2}}{d_{k}}}} & {\left( {{Equation}\quad 9} \right),}\end{matrix}$

where b_(k) and d_(k) are vector elements given by $\begin{matrix}{{b = {\begin{pmatrix}b_{1} \\b_{2} \\\vdots \\b_{M}\end{pmatrix} = {L^{H}{a(\theta)}}}}\quad {and}} & \left( {{Equation}\quad 10} \right) \\{D = \begin{pmatrix}d_{1} & 0 & \cdots & 0 \\0 & d_{2} & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & 0 \\0 & \cdots & 0 & d_{M}\end{pmatrix}} & {\left( {{Equation}\quad 11} \right),}\end{matrix}$

respectively. The lower triangular matrix has been used in the presentembodiment; however, an upper triangular matrix also obviously producesa similar advantage.

Additionally, correlation matrix calculation unit 7 may apply a spatialsmoothing technique to the correlation matrix in order to suppresscorrelation wave. The method in the present embodiment can be similarlyapplied in this case if the spatially smoothed correlation matrixinstead of correlation matrix R is fed into direction estimatingprocessor 12.

An example of an array antenna having a constant-interval linear arrayshape is described in M. Haardt and J. A. Nossek, “Unitary ESPRIT: Howto Obtain Increased Estimation Accuracy with a Reduced CommutationalBurden,” IEEE Trans. Signal Processing, vol. 43, No. 5, pp. 1232-1242(1995). In this example, thanks to the conjugation center symmetry of aphase of a steering vector, the steering vector can be converted into areal vector using unitary matrix Q_(M) written as

b(θ)=Q _(M) ^(H) a(θ)  (Equation 12)

where a(θ) is a steering vector when the phase center matches with thearray center.

A method similar to the method in the present embodiment can be appliedto this case, if direction estimating processor 12 uses the real part ofQ_(M) ^(H)RQ_(M) instead of correlation matrix R, and b(θ) instead ofsteering vector a(θ).

When an array antenna having a linear array shape is employed,estimation accuracy in the end fire direction decreases. Therefore,arrival-angle evaluation unit 10 sets the angle interval in the end firedirection of the array antenna to be larger than that in the bore-sightdirection, and calculates an evaluation value of the arrival-angleevaluation function. The calculation amount can be thus reduced. Herethe bore-sight direction means the direction of the normal to the lineararray arrangement direction.

A configuration may be employed that comprises, instead of receivingunits 3 and A/D converters 5 in the present embodiment, the followingcomponents:

intermediate frequency (IF) receiving units for converting frequenciesand detecting phases of RF signals supplied from respective antennaelements 1—1 to 1-M and outputting IF signals;

IF A/D converters for converting the IF signals to digital signals; and

digital orthogonal wave detectors for orthogonally demodulating thedigital signals and supplying complex digital signals to the correlationmatrix calculation unit.

2. Second Exemplary Embodiment

FIG. 4 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

Operations until correlation matrix R is fed into direction estimatingprocessor 12 a are similar to those in embodiment 1. Inverse matrixcalculation unit 20 calculates inverse matrix R⁻¹ of correlation matrixR. Because inverse matrix R⁻¹ is a positive definite matrix, triangularmatrix calculation unit 21 derives lower triangular matrix L written as

 R ⁻¹ =L L ^(H)  (Equation 13),

using the cholesky factorization.

Using lower triangular matrix L, arrival-angle evaluation unit 22converts a conventional arrival-angle evaluation function obtained byCapon method as given by $\begin{matrix}{{{Fc}(\theta)} = \frac{1}{{a^{H}(\theta)}R^{- 1}{a(\theta)}}} & {\left( {{Equation}\quad 14} \right),}\end{matrix}$

to an evaluation function $\begin{matrix}{{{Fc}_{2}(\theta)} = \frac{1}{{\quad {L^{H}{a(\theta)}}}^{2}}} & {\left( {{Equation}\quad 15} \right),}\end{matrix}$

where, ∥x∥ is the norm of vector x, and a(θ) is a normalized steeringvector of the array antenna. Arrival-angle evaluation unit 22 thenevaluates an arrival angle every predetermined angle step Δθ using theevaluation function given by Eq.15. Here, the arrival-angle evaluationfunction given by Eq.14 is described in J. Capon, “High-ResolutionFrequency-Wavenumber Spectrum Analysis.” Proc. IEEE, 57 (8), pp.1408-1418, 1969.

Since elements outside the lower triangular part in lower triangularmatrix L are null, the sum-of-product calculation amount for thearrival-angle evaluation function given by Eq.15 is ratio (M+3)/[2(M+1)]lower than that for the conventional arrival-angle evaluation functiongiven by Eq.14. A relation between the calculation amount for thecholesky factorization and that of Fc₂(θ_(i)) for one arrival angleθ_(i) given by Eq.15 is similar to that given by embodiment 1.Therefore, an increment of the calculation amount caused by the choleskyfactorization can be considered sufficiently smaller than a decrement ofthe calculation amount for the arrival-angle evaluation in the entireangle range in Eq.15.

Arrival-angle determination unit 23 detects a peak direction based on anarrival-angle evaluation result every Δθ in a variable range of θ, anduses the detected direction as an arrival-angle estimation value of theincident waves.

In the present embodiment, using arrival-angle evaluation functionFc₂(θ) (Eq.15), the calculation amount in the arrival-angle evaluationcan be reduced compared with the arrival-angle evaluation function(Eq.14) by the Capon method. Function Fc₂(θ) has been derived byequivalent conversion of the arrival-angle evaluation function given byEq.14, using lower triangular matrix L determined in triangular matrixcalculation unit 21 by applying the cholesky factorization to inversematrix R⁻¹ of the correlation matrix.

The direction estimation based on the Capon method has been discussedabove. However, the method of the present embodiment can be as-isapplied to a received signal sampled every frequency when the delay timeof the received wave is estimated at high resolution. That is because anevaluation function similar to that in Eq.14 is used.

Additionally, correlation matrix calculation unit 7 can apply a spatialsmoothing technique to the correlation matrix in order to suppresscorrelation wave. The method of the present embodiment can be similarlyapplied to this case, if the spatially smoothed correlation matrixinstead of correlation matrix R is fed into the direction estimatingprocessor.

When an array antenna having the constant-interval linear array shape isemployed, a steeling vector can be converted into a real vector usingunitary matrix Q_(M) given by Eq.12, thanks to the conjugation centersymmetry of the phase of the steeling vector. In Eq.12, a(θ) is asteering vector when the phase center matches with the array center. Amethod similar to the method in the present embodiment can be applied tothis case, if direction estimating processor 12 a uses the real part ofQ_(M) ^(H)RQ_(M) instead of correlation matrix R, and b(θ) instead ofsteering vector a(θ).

When an array antenna having the linear array shape is employed,estimation accuracy in the bore-sight direction decreases. Therefore,arrival-angle evaluation unit 22 sets the angle interval in the end filedirection of the array antenna to be larger than that in the bore-sightdirection, and calculates an evaluation value of the arrival-angleevaluation function. The calculation amount can be thus reduced.

Additionally, triangular matrix calculation unit 21 may derive lowertriangular matrix L and diagonal matrix D using the modified choleskyfactorization. The modified cholesky factorization does not require thesquare root calculation, so that the calculation time can be reduced.

3. Third Exemplary Embodiment

FIG. 5 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

Operations until correlation matrix R are fed into direction estimatingprocessor 12 b are similar to those in embodiment 1.

Since correlation matrix R is a positive definite matrix, triangularmatrix calculation unit 24 derives lower triangular matrix L given by

R=L L^(H)  (Equation 16),

using the cholesky factorization.

Inverse matrix calculation unit 25 calculates inverse matrix L⁻¹ oflower triangular matrix L.

Using lower triangular matrix L, arrival-angle evaluation unit 26converts the arrival-angle evaluation function (Eq.14) derived by theCapon method to an evaluation function Fc₃(θ) expressed as$\begin{matrix}{{{Fc}_{3}(\theta)} = \frac{1}{{\quad {L^{- 1}{a(\theta)}}}^{2}}} & {\left( {{Equation}\quad 17} \right),}\end{matrix}$

where, ∥x∥ is the norm of vector x, and a(θ) is a normalized steeringvector of the array antenna. Arrival-angle evaluation unit 26 thenevaluates an arrival angle every predetermined angle step Δθ using theevaluation function of Fc₃(θ).

Since elements outside the lower triangular part in lower triangularmatrix L are null, the sum-of-product calculation amount for thearrival-angle evaluation function given by Eq.17 is ratio (M+3)/[2(M+1)]lower than that for the Capon method's conventional arrival-angleevaluation function (Eq.14). A relation between the calculation amount(Eq.16) for the cholesky factorization and that of Fc₂(θ_(i)) perarrival angle θ_(i) is similar to that shown in embodiment 1. Therefore,an increment of the calculation amount caused by the choleskyfactorization can be considered sufficiently smaller than a decrement ofthe calculation amount for the arrival-angle evaluation in the entireangle range in Eq.17.

Arrival-angle determination unit 27 detects a peak direction based on anarrival-angle evaluation result every Δθ in a variable range of θ, anduses the detected direction as an arrival-angle estimation value of theincident waves.

In the present embodiment, using arrival-angle evaluation functionFc₃(θ) (Eq.17), the calculation amount in the arrival-angle evaluationcan be significantly reduced compared with the conventionalarrival-angle evaluation function (Eq.14) by the Capon method. FunctionFc₃(θ) has been derived by equivalent conversion of the arrival-angleevaluation function given by Eq.14, using lower triangular matrix Ldetermined in triangular matrix calculation unit 24 by applying thecholesky factorization to correlation matrix R.

The direction estimation based on the Capon method has been discussedabove. However, the method of the present embodiment can be as-isapplied to a received signal sampled every frequency when the delay timeof the received wave is estimated at high resolution. That is because anevaluation function similar to that in Eq.14 is used.

Additionally, correlation matrix calculation unit 7 can apply a spatialsmoothing technique to the correlation matrix in order to suppresscorrelation wave. The method of the present embodiment can be similarlyapplied to this case, if the spatially smoothed correlation matrixinstead of correlation matrix R is fed into the direction estimatingprocessor.

When an array antenna having the constant-interval linear array shape isemployed, a steering vector can be converted into a real vector usingunitary matrix Q_(M) given by Eq.12, thanks to the conjugation centersymmetry of the phase of the steering vector. In Eq.12, a(θ) is asteering vector when the phase center matches with the array center. Amethod similar to the method in the present embodiment can be applied tothis case, if direction estimating processor 12 b uses the real part ofQ_(M) ^(H)RQ_(M) instead of correlation matrix R, and b(θ) instead ofsteering vector a(θ).

When an array antenna having the linear array shape is employed,estimation accuracy in the bore-sight direction decreases. Therefore,arrival-angle evaluation unit 26 sets the angle interval in the end firedirection of the array antenna to be larger than that in the bore-sightdirection, and calculates an evaluation value of the arrival-angleevaluation function. The calculation amount can be thus reduced.

Additionally, triangular matrix calculation unit 24, using the modifiedcholesky factorization, may derive lower triangular matrix L anddiagonal matrix D given by

R=L D L^(H)  (Equation 18).

The modified cholesky factorization does not require the square rootcalculation, so that the calculation time can be reduced.

An arrival-angle evaluation function in this case is expressed as$\begin{matrix}{{{Fc}_{3}(\theta)} = \frac{1}{\sum\limits_{k = 1}^{M}\quad \frac{b_{k}^{2}}{d_{k}}}} & {\left( {{Equation}\quad 19} \right),}\end{matrix}$

where b_(k) and d_(k) are vector elements given by $\begin{matrix}{{b = {\begin{pmatrix}b_{1} \\b_{2} \\\vdots \\b_{M}\end{pmatrix} = {L^{- 1}{a(\theta)}}}}\quad {and}} & \left( {{Equation}\quad 20} \right) \\{D = \begin{pmatrix}d_{1} & 0 & \cdots & 0 \\0 & d_{2} & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & 0 \\0 & \cdots & 0 & d_{M}\end{pmatrix}} & {\left( {{Equation}\quad 21} \right),}\end{matrix}$

respectively. The lower triangular matrix has been used in the presentembodiment; however, an upper triangular matrix also obviously producesa similar advantage.

4. Fourth Exemplary Embodiment

FIG. 6 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

Operations until correlation matrix R are fed into direction estimatingprocessor 12 c is similar to those in embodiment 1.

Since correlation matrix R is a positive definite matrix, triangularmatrix calculation unit 28, using the cholesky factorization, deriveslower triangular matrix L given by

R=L L^(H)  (Equation 22).

Using lower triangular matrix L, arrival-angle evaluation unit 29converts conventional arrival-angle evaluation function F_(F)(θ)obtained by Fourier method as given by

F _(F)(θ)=a ^(H)(θ)Ra(θ)  (Equation 23),

to an evaluation function expressed as

F _(F2)(θ)=∥L ^(H) a(θ)∥²  (Equation 24),

where, ∥x∥ is the norm of vector x, and a(θ) is a normalized steeringvector of the array antenna. Arrival-angle evaluation unit 29 thenevaluates an arrival angle every predetermined angle step Δθ using theevaluation function given by Eq.24. Here, the arrival-angle evaluationfunction given by Eq.23 is described in M. S. Bartlett. “SmoothingPeriodograms from Time Series with Continuous Spectra.” Nature, 161, pp.686-687, (1948).

Since elements outside the lower triangular part in lower triangularmatrix L are null, the sum-of-product calculation amount for thearrival-angle evaluation function given by Eq.24 is ratio (M+3)/[2(M+1)]lower than that for the conventional arrival-angle evaluation functiongiven by Eq.23. An increment of the calculation amount caused by thecholesky factorization is sufficiently smaller than a decrement of thecalculation amount for the arrival-angle evaluation in the entire anglerange in Eq.24. That is because the relation between the calculationamounts in the present embodiment is also similar to that shown inembodiment 1.

Arrival-angle determination unit 30 detects a peak direction based on anarrival-angle evaluation result every Δθ in a variable range of θ, anduses the detected direction as an arrival-angle estimation value of theincident waves.

In the present embodiment, using arrival-angle evaluation functionF_(F2)(θ) (Eq.24), the calculation amount in the arrival-angleevaluation can be significantly reduced compared with the conventionalarrival-angle evaluation function (Eq.23) by Fourier method. FunctionF_(F2)(θ) has been derived by equivalent conversion of the arrival-angleevaluation function given by Eq.23, using lower triangular matrix Ldetermined in the triangular matrix calculation unit by applying thecholesky factorization to the correlation matrix.

Additionally, correlation matrix calculation unit 7 can apply a spatialsmoothing technique to the correlation matrix in order to suppresscorrelation wave. The method of the present embodiment can be similarlyapplied to this case, if the spatially smoothed correlation matrixinstead of correlation matrix R is fed into direction estimatingprocessor 12 c.

When an array antenna having the constant-interval linear array shape isemployed, a steering vector can be converted into a real vector usingunitary matrix Q_(M) given by Eq.12, thanks to the conjugation centersymmetry of the phase of the steering vector. In Eq.12, a(θ) is asteering vector when the phase center matches with the array center. Amethod similar to the method in the present embodiment can be applied tothis case, if direction estimating processor 12 c uses the real part ofQ_(M) ^(H)RQ_(M) instead of correlation matrix R, and b(θ) instead ofsteering vector a(θ).

When an array antenna having the linear array shape is employed,estimation accuracy in the bore-sight direction decreases. Therefore,arrival-angle evaluation unit 30 sets the angle interval in the end firedirection of the array antenna to be larger than that in the bore-sightdirection, and calculates an evaluation value of the arrival-angleevaluation function. The calculation amount can be thus reduced.

Additionally, triangular matrix calculation unit 28, using the modifiedcholesky factorization, may derive lower triangular matrix L anddiagonal matrix D given by Eq.18. The modified cholesky factorizationdoes not requite the square root calculation, so that the calculationtime can be reduced. An arrival-angle evaluation function in this caseis expressed as $\begin{matrix}{{F_{F3}(\theta)} = {\sum\limits_{k = 1}^{M}\quad \frac{b_{k}^{2}}{d_{k}}}} & {\left( {{Equation}\quad 25} \right),}\end{matrix}$

where b_(k) and d_(k) are vector elements written as $\begin{matrix}{{b = {\begin{pmatrix}b_{1} \\b_{2} \\\vdots \\b_{M}\end{pmatrix} = {L^{H}{a(\theta)}}}}\quad {and}} & \left( {{Equation}\quad 26} \right) \\{D = \begin{pmatrix}d_{1} & 0 & \cdots & 0 \\0 & d_{2} & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & 0 \\0 & \cdots & 0 & d_{M}\end{pmatrix}} & {\left( {{Equation}\quad 27} \right),}\end{matrix}$

respectively. The lower triangular matrix has been used in the presentembodiment; however, an upper triangular matrix also obviously producesa similar advantage.

5. Fifth Exemplary Embodiment

FIG. 7 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

Operations until complex digital signals 6 are obtained are similar tothose in embodiment 1.

Correlation vector calculation unit 31 selects one of complex digitalsignals 6, and performs a correlation calculation between an antennaelement—a reference antenna—corresponding to the selected signal andanother antenna element, thereby deriving a correlation vector. Anexample will be described hereinafter employing antenna element 1—1 asthe reference antenna. Antenna elements 1—1 to 1-M receive sampling datax₁ (k), x₂ (k), . . . x_(M) (k) at sampling time t₀+kΔT, respectively.Here t₀ is an arbitrary time, ΔT is a sampling interval, and k is anatural number. Correlation vector calculation unit 31, using snapshotdata of the sampling data for k=1 to N, derives M-dimensionalcorrelation vector Rv expressed as $\begin{matrix}{R_{v} = {\frac{1}{N}{\sum\limits_{k = 1}^{N}{{x_{1}(k)}^{*}{x^{T}(k)}}}}} & {\left( {{Equation}\quad 28} \right),}\end{matrix}$

where asterisk * shows complex conjugate.

Arrival-angle evaluation unit 32 evaluates an arrival angle everypredetermined angle step Δθ using the evaluation function given by

F _(v)(θ)=∥R _(v) ^(H) a(θ)∥  (Equation 29),

where, ∥x∥ is the norm of vector x, and a(θ) is a normalized steeringvector of the array antenna.

Arrival-angle determination unit 33 detects a peak direction based on anarrival-angle evaluation result every Δθ in a variable range of θ, anduses the detected direction as an arrival-angle estimation value of theincident waves.

The arrival angle is evaluated using the correlation vector instead ofthe correlation matrix in the present embodiment, so that thecalculation amount in the arrival-angle evaluation can be significantlyreduced compared with the conventional Fourier method (Eq.23).

When an array antenna having the linear array shape is employed,estimation accuracy in the bore-sight direction decreases. Therefore,arrival-angle evaluation unit 32 sets the angle interval in the end firedirection of the array antenna to be larger than that in the bore-sightdirection, and calculates an evaluation value of the arrival-angleevaluation function. The calculation amount can be thus reduced.

6. Sixth Exemplary Embodiment

FIG. 8 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter. The present embodiment employs an array antenna having theconstant-interval linear array shape.

Operations until complex digital signals 6 are obtained are similar tothose in embodiment 1. Correlation vector calculation unit 34 selectsone of complex digital signals 6, and performs a correlation calculationbetween an antenna element—a reference antenna—corresponding to theselected signal and another antenna element, thereby deriving acorrelation vector. An example will be described hereinafter employingantenna element 1—1 as the reference antenna. Antenna elements 1—1 to1-M receive sampling data x₁ (k), x₂ (k), . . . , x_(M) (k) at samplingtime t₀+kΔT, respectively. Here t₀ is an arbitrary time, ΔT is asampling interval, and k is a natural number. Correlation vectorcalculation unit 34, using snapshot data of the sampling data for k=1 toN, derives M-dimensional correlation vector Rv expressed as Eq.28. InEq.28, asterisk * shows complex conjugate.

Since the array antenna has the constant-interval linear array shape, asteering vector can be converted into a real vector using unitary matrixQ_(M) given by Eq.12, thanks to the conjugation center symmetry of thephase of the steering vector. In Eq.12, a(θ) is a steering vector whenthe phase center matches with the array center. Unitary transformingunit 35 unitary-transforms correlation vector Rv as in

R _(r 1)=real(q _(1,l) R v Q _(M))  (Equation 30),

R _(r 2)=real(q* _(1,m) R v Q _(M))  (Equation 31),

where q_(i,j) is (i, j) element of matrix Q_(M), real (x) is a vectorcomprising real parts of respective elements of vector x, and m is M/2+1for even M (number of elements), or m is (M+1)/2+1 for odd M.

Arrival-angle evaluation unit 36 evaluates an arrival angle everypredetermined angle step Δθ using the evaluation function given by

F _(v2)(θ)=[b ₁(θ)R _(r1) +b _(m)(θ)R _(r2) ]b(θ)  (Equation 32),

where, real steering vector b(θ) is converted from steering vector a(θ)using Eq.12, and b_(k)(θ) is the k-th element of real steering vectorb(θ).

Arrival-angle determination unit 37 detects a peak direction based on anarrival-angle evaluation result every Δθ in a variable range of θ, anduses the detected direction as an arrival-angle estimation value of theincident waves.

The arrival angle is evaluated using the correlation vector instead ofthe correlation matrix and using the real steering vector in the presentembodiment, so that the calculation amount in the arrival-angleevaluation can be significantly reduced compared with the conventionalFourier method (Eq.23).

When an array antenna having the linear array shape is employed,estimation accuracy in the bore-sight direction decreases. Therefore,arrival-angle evaluation unit 37 sets the angle interval in the end firedirection of the array antenna to be larger than that in the bore-sightdirection, and calculates an evaluation value of the arrival-angleevaluation function. The calculation amount can be thus reduced.

7. Seventh Exemplary Embodiment

FIG. 9 is a block diagram illustrating the other configuration ofarrival-angle evaluation unit 10 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thearrival-angle evaluation unit in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

The present embodiment assumes that antenna elements 1—1 to 1-M of arrayantenna 1 are arranged linearly at a constant interval. Operations untiltriangular matrix L is fed into arrival-angle evaluation unit 10 a aresimilar to those in embodiment 1.

Arrival-angle evaluation unit 10 a comprises the following components:

positive-region evaluation unit 40 for calculating an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) using thebore-sight direction of the array antenna as an angle reference (θ=0),because the array antenna has the constant-interval linear array shape;and

negative-region evaluation unit 41 for converting the evaluation resultof the positive-region evaluation unit to an arrival-angle evaluationvalue in the negative angle region (−90°≦θ≦0°).

Since the array antenna has the constant-interval linear array shape,steering vector a(θ) is a complex vector expressed as $\begin{matrix}{{a(\theta)} = \begin{bmatrix}{\exp \left\{ {{- {j2}}\quad \pi \quad {d \cdot 0 \cdot \sin}\quad {\theta/\lambda}} \right\}} \\{\exp \left\{ {{- {j2}}\quad \pi \quad {d \cdot 1 \cdot \sin}\quad {\theta/\lambda}} \right\}} \\{\quad \vdots} \\{\exp \left\{ {{- {j2}}\quad \pi \quad {d \cdot \left( {M - 1} \right) \cdot \sin}\quad {\theta/\lambda}} \right\}}\end{bmatrix}} & {\left( {{Equation}\quad 33} \right).}\end{matrix}$

The real part of the complex vector is an even function of θ, and theimaginary part is an odd function of θ. Using this feature, Eq.7 can betransformed to $\begin{matrix}\begin{matrix}{{F_{2}\left( {\pm \theta_{l}} \right)} = \left\lbrack {{L^{H}{a\left( {\pm \theta_{l}} \right)}}} \right\rbrack^{- 2}} \\{= \left\lbrack {{\left( {{{Re}\left( L^{H} \right)} + {j\quad {{Im}\left( L^{H} \right)}}} \right) \cdot \left( {{{Re}\left( {a\left( \theta_{l} \right)} \right)} \pm {j\quad {{Im}\left( {a\left( \theta_{l} \right)} \right)}}} \right)}} \right\rbrack^{- 2}} \\{= \left\lbrack {{\left( {{{{Re}\left( L^{H} \right)} \cdot {{Re}\left( {a\left( \theta_{l} \right)} \right)}} \mp {{{Im}\left( L^{H} \right)}\quad \cdot {{Im}\left( {a\left( \theta_{l} \right)} \right)}}} \right.^{2} -}} \right.} \\\left. {{{{{Im}\left( L^{H} \right)} \cdot {{Re}\left( {a\left( \theta_{l} \right)} \right)}} \pm {{{Re}\left( L^{H} \right)} \cdot {{Im}\left( {a\left( \theta_{l} \right)} \right)}}}}^{2} \right\rbrack^{- 1} \\{= \left\lbrack {{{{c\quad 1} \mp {c\quad 2}}}^{2} - {{{c\quad 3} \pm {c\quad 4}}}^{2}} \right\rbrack^{- 1}}\end{matrix} & {\left( {{Equation}\quad 34} \right),}\end{matrix}$

for θ₁ satisfying 0°≦θ₁≦90°. Here, Re(x) is a vector comprising realparts of respective elements of the complex vector (or matrix) x, Im(x)is a vector comprising imaginary parts of them, d is an interval ofantenna elements, λ is a wavelength of carrier frequency, and vectorsc1, c2, c3, c4 are given by

c1=Re(L ^(H))·Re(a(θ₁))  (Equation 35),

c2=Im(L ^(H))·Im(a(θ₁))  (Equation 36),

c3=Im(L ^(H))·Re(a(θ₁))  (Equation 37),

and

c4=Re(L ^(H))·Im(a(θ₁))  (Equation 38),

respectively.

Positive-region evaluation unit 40 calculates an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) atpredetermined angle step Δθ using the relation discussed above.Positive-region evaluation unit 40 firstly calculates vectors c1, c2,c3, c4, and then derives a positive-region arrival-angle evaluationvalue in accordance with

 F3(θ₁)=[∥c1−c2∥² −∥c3+c4∥²]⁻¹  (Equation 39).

Evaluation unit 40 outputs resultant values of vectors c1, c2, c3, c4 tonegative-region evaluation converter 41.

Negative-region evaluation converter 41 calculates an arrival-angleevaluation value in the −θ₁ direction using vectors c1, c2, c3, c4supplied from evaluation unit 40 in accordance with

F4(−θ₁)=[∥c1+c2∥² −∥c3−c4∥²]⁻¹  (Equation 40).

Arrival-angle determination unit 11 detects a peak direction based on anarrival-angle evaluation result of arrival-angle evaluation unit 10 aevery Δθ in a variable range of θ, and uses the detected direction as anarrival-angle estimation value of the incident waves.

In the present embodiment, the positive-region arrival-angle evaluationvalue can be converted to the negative-region arrival-angle evaluationvalue using vectors c1, c2, c3, c4, when the array antenna having theconstant-interval linear array shape is employed. Here the vectors c1,c2, c3, c4 are calculated when the positive-region arrival-angleevaluation value is derived. The calculation amount in the arrival-angleevaluation can be further reduced substantially in half.

The present embodiment has been described using the arrival-angleevaluation function given by Eq.7 in embodiment 1. When an array antennahaving the constant-interval linear array shape is employed, a similartransformation can be also applied to the arrival-angle evaluationfunction using steering vector a(θ) in the other embodiment. Theconversion to the negative-region arrival-angle evaluation value isallowed using vectors c1, c2, c3, c4 calculated when the positive-regionarrival-angle evaluation value are derived, as discussed above. Thecalculation amount in the arrival-angle evaluation can be reducedsubstantially in half compared with the conventional method.

8. Eighth Exemplary Embodiment

FIG. 10 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

The present embodiment assumes that antenna elements 1—1 to 1-M of arrayantenna 1 are arranged linearly at a constant interval. Operations untilcorrelation matrix calculation unit 7 outputs correlation matrix R aresimilar to those in embodiment 1.

Unitary transforming unit 42 transforms correlation matrix R as given by

R r=real(Q _(M) ^(H) R Q _(M))  (Equation 41),

using unitary matrix Q_(M) for converting a steering vector employingthe phase center as the array center to a real vector. Here real(A) is amatrix comprising real parts of respective elements of matrix A.

Noise spatial eigenmatrix calculation unit 8 a applies the eigenvaluefactorization to unitary-transformed correlation matrix Rr by unitarytransforming unit 42 to derive eigenvalues λ₁-λ_(M) in the descendingorder and eigenvactors e₁-e_(M) corresponding to them. When a number ofthe incident waves is S, calculation unit 8 a outputs noise spatialeigenmatrix E_(N)=[e_(S+1), . . . , e_(M)] comprising (M−S)eigenvactors, namely column vectors, belonging to a noise partial spacehaving the relation given by Eq.3.

Triangular matrix calculation unit 9 a derives product U of a noisespatial eigenmatrix and a complex-conjugated and transposed matrix of itas in Eq.5. Triangular matrix calculation unit 9 a derives lowertriangular matrix L given by Eq.6 using the cholesky factorization,because matrix U is an M×M positive definite matrix.

Arrival-angle evaluation unit 10 a comprises the following components:

positive-region evaluation unit 40 a for calculating the arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) using thebore-sight direction of the array antenna as an angle reference (θ=0),because the array antenna has the constant-interval linear array shape;and

negative-region evaluation unit 41 a for converting the evaluationresult of the positive-region evaluation unit to an arrival-angleevaluation value in the negative angle region (−90°≦θ≦0°).

When steering vector a(θ) employing the phase center as the array centeris converted using unitary matrix Q_(M), real vector b(θ) is derived asin $\begin{matrix}\begin{matrix}{{b(\theta)} = {\sqrt{2}\left\lbrack {{\cos \left( {\frac{M - 1}{2}\mu} \right)},\quad \ldots \quad,{\cos (\mu)},{- {\sin \left( {\frac{M - 1}{2}\mu} \right)}},\quad \ldots \quad,{- {\sin (\mu)}}} \right\rbrack}^{T}} \\{{{for}\quad M} = {2\quad m\quad {or}}} \\{{b(\theta)} = {\sqrt{2}\left\lbrack {{\cos \left( {\frac{M - 1}{2}\mu} \right)},\quad \ldots \quad,{\cos (\mu)},\frac{1}{\sqrt{2}},{- {\sin \left( {\frac{M - 1}{2}\mu} \right)}},\quad \ldots \quad,{- {\sin (\mu)}}} \right\rbrack}^{T}} \\{{{{for}\quad M} = {{2\quad m} + 1}},}\end{matrix} & {\left( {{Equation}\quad 42} \right),}\end{matrix}$

where μ is written as $\begin{matrix}{\mu = {{- \frac{2\quad \pi}{\lambda}}d\quad \sin \quad \theta}} & {\left( {{Equation}\quad 43} \right),}\end{matrix}$

where, d is an interval between the antenna elements, and λ is awavelength of carrier frequency.

When number M of antenna elements equals 2m, b(θ) is an even functionfor elements 1 to m or an odd function for elements m+1 to 2m, as shownin Eq.42. Using this feature, Eq.7 can be transformed to$\begin{matrix}\begin{matrix}{{F\quad 2\left( {\pm \theta_{l}} \right)} = \left\lbrack {{L^{H}{b\left( {\pm \theta_{l}} \right)}}} \right\rbrack^{- 2}} \\{= \left\lbrack {{{L^{H}{b_{even}\left( \theta_{l} \right)}} \pm {L^{H}{b_{odd}\left( \theta_{l} \right)}}}} \right\rbrack^{- 2}} \\{= \left\lbrack {{{c\quad 1} \pm {c\quad 2}}} \right\rbrack^{- 2}}\end{matrix} & \left( {{Equation}\quad 44} \right)\end{matrix}$

for θ₁ satisfying 0°≦θ₁≦90°. Here, c1, c2, b_(even)(θ), and b_(odd)(θ)are given by $\begin{matrix}{{c\quad 1} = {L^{H}{b_{even}\left( \theta_{l} \right)}}} & {\left( {{Equation}\quad 45} \right),} \\{{c\quad 2} = {L^{H}{b_{odd}\left( \theta_{l} \right)}}} & {\left( {{Equation}\quad 46} \right),} \\{{{b_{even}(\theta)} = {\sqrt{2}\left\lbrack {{\cos \left( {\frac{M - 1}{2}\mu} \right)},\quad \ldots \quad,{\cos (\mu)},0,\quad \ldots \quad,0} \right\rbrack}^{T}}{and}} & {\left( {{Equation}\quad 47} \right),} \\{{b_{odd}(\theta)} = {\sqrt{2}\left\lbrack {0,\quad \ldots \quad,0,{- {\sin \left( {\frac{M - 1}{2}\mu} \right)}},\quad \ldots \quad,{- {\sin (\mu)}}} \right\rbrack}^{T}} & {\left( {{Equation}\quad 48} \right),}\end{matrix}$

respectively.

When number M of antenna elements equals 2 m+1, b(θ) is an even functionfor elements 1 to m, and b(θ) is an odd function for elements m+2 to M.Using this feature, Eq.7 can be transformed to Eq.44, for θ₁ satisfying0°≦θ₁≦90°. In this case, b_(even)(θ) and b_(odd)(θ) are given by$\begin{matrix}{{{b_{even}(\theta)} = {\sqrt{2}\left\lbrack {{\cos \left( {\frac{M - 1}{2}\mu} \right)},\quad \ldots \quad,{\cos (\mu)},{\frac{1}{\sqrt{2}}0},\quad \ldots \quad,0} \right\rbrack}^{T}}{and}} & {\left( {{Equation}\quad 49} \right),} \\{{b_{odd}(\theta)} = {\sqrt{2}\left\lbrack {0,\quad \ldots \quad,0,{- {\sin \left( {\frac{M - 1}{2}\mu} \right)}},\quad \ldots \quad,{- {\sin (\mu)}}} \right\rbrack}^{T}} & {\left( {{Equation}\quad 50} \right),}\end{matrix}$

respectively.

Positive-region evaluation unit 40 a calculates an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) atpredetermined angle step Δθ using the relation discussed above.Positive-region evaluation unit 40 a firstly calculates vectors c1, c2(Eq.45 and Eq.46) and then derives a positive-region arrival-angleevaluation value in accordance with

 F3(θ₁)=[∥c1+c2∥²]⁻¹  (Equation 51).

Evaluation unit 40 a outputs resultant values of vectors c1, c2 tonegative-region evaluation converter 41 a.

Negative-region evaluation converter 41 a calculates an arrival-angleevaluation value in the −θ₁ direction using vectors c1, c2 supplied fromevaluation unit 40 a in accordance with

F4(−θ₁)=[∥c1−c2∥²]⁻¹  (Equation 52).

Arrival-angle determination unit 11 a detects a peak direction based onan arrival-angle evaluation result of arrival-angle evaluation unit 10 aevery Δθ in the variable range of θ, and uses the detected direction asan arrival-angle estimation value of the incident waves.

In the present embodiment, the array antenna having theconstant-interval linear array shape has been employed, and the realsteering vector has been derived by unitary matrix transformation. Thepositive-region arrival-angle evaluation value can be converted to thenegative-region arrival-angle evaluation value, using vectors c1, c2calculated when the positive-region arrival-angle evaluation value arederived. The calculation amount in the arrival-angle evaluation can bereduced substantially in half compared with embodiment 1.

9. Nineth Exemplary Embodiment

FIG. 11 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

The present embodiment assumes that antenna elements 1—1 to 1-M of arrayantenna 1 are arranged linearly at a constant interval. Operations untilcorrelation matrix calculation unit 7 outputs correlation matrix R aresimilar to those in embodiment 1.

Unitary transforming unit 42 transforms correlation matrix R as given byEq.41, using unitary matrix Q_(M) for converting a steering vectoremploying the phase center as the array center to a real vector. Inversematrix calculation unit 20 a calculates an inverse matrix ofunitary-transformed correlation matrix Rr derived by the unitarytransforming unit. Triangular matrix calculation unit 21 a derives lowertriangular matrix L given by Eq.13 using the cholesky factorization.That is because inverse matrix R⁻¹ is a positive definite matrix.

Arrival-angle evaluation unit 22 a comprises the following components:

positive-region evaluation unit 53 for calculating an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) using thebore-sight direction of the array antenna as an angle reference (θ=0),because the array antenna has the constant-interval linear array shape;and

negative-region evaluation unit 54 for converting the evaluation resultof the positive-region evaluation unit to an arrival-angle evaluationvalue in the negative angle region (−90°≦θ≦0°).

Positive-region evaluation unit 53 calculates an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) atpredetermined angle step Δθ. Positive-region evaluation unit 53 firstlycalculates vectors c1, c2 given by Eq.45 and Eq.46 for θ₁ satisfying0°≦θ₁≦90° and then derives a positive-region arrival-angle evaluationvalue in accordance with

F _(C2)(θ₁)=[∥c1+c2∥²]⁻¹  (Equation 53).

Evaluation unit 53 outputs resultant values of vectors c1, c2 tonegative-region evaluation converter 54.

Negative-region evaluation converter 54 calculates an arrival-angleevaluation value in the −θ₁ direction using vectors c1, c2 supplied fromevaluation unit 53 in accordance with

F _(c2)(−θ₁)=[∥c1−c2∥²]⁻¹  (Equation 54).

Arrival-angle determination unit 23 detects a peak direction based on anarrival-angle evaluation result of arrival-angle evaluation unit 22 aevery Δθ in the variable range of θ, and uses the detected direction asan arrival-angle estimation value of the incident waves.

In the present embodiment, the array antenna having theconstant-interval linear array shape has been employed, and the realsteering vector has been derived by unitary matrix transformation. Thepositive-region arrival-angle evaluation value can be converted to thenegative-region arrival-angle evaluation value using vectors c1, c2calculated when the positive-region arrival-angle evaluation value arederived. The calculation amount in the arrival-angle evaluation can bereduced substantially in half compared with embodiment 1.

The present embodiment can be similarly applied to the arrival-angleevaluation function described in embodiment 3.

10. Tenth Exemplary Embodiment

FIG. 12 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

The present embodiment assumes that antenna elements 1—1 to 1-M of arrayantenna 1 are arranged linearly at a constant interval. Operations untilcorrelation matrix calculation unit 7 outputs correlation matrix R aresimilar to those in embodiment 1.

Unitary transforming unit 42 transforms correlation matrix R as given byEq.41, using unitary matrix Q_(M) for converting a steering vectoremploying the phase center as the array center to a real vector.Triangular matrix calculation unit 24 a derives lower triangular matrixL using the cholesky factorization, because unitary-transformedcorrelation matrix Rr is a positive definite matrix.

Arrival-angle evaluation unit 25 a comprises the following components:

positive-region evaluation unit 55 for calculating an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) using thebore-sight direction of the array antenna as an angle reference (θ=0),because the array antenna has the linear array shape; and

negative-region evaluation unit 56 for converting the evaluation resultof the positive-region evaluation unit to an arrival-angle evaluationvalue in the negative angle region (−90°≦θ≦0°).

Positive-region evaluation unit 55 calculates an arrival-angleevaluation function in the positive angle region (0°≦θ≦90°) atpredetermined angle step Δθ. Positive-region evaluation unit 55 firstlycalculates vectors c1, c2 given by Eq.45 and Eq.46 for θ₁ satisfying0°≦θ₁≦90° and then derives a positive-region arrival-angle evaluationvalue in accordance with

F _(F2)(θ₁)=∥c1+c2∥²  (Equation 55).

Evaluation unit 55 outputs respective resultant values of vectors c1, c2to negative-region evaluation converter 56.

Negative-region evaluation converter 56 calculates an arrival-angleevaluation value in the −θ₁ direction using vectors c1, c2 supplied fromevaluation unit 55 in accordance with

F _(F2)(−θ₁)=∥c1−c2∥²  (Equation 56).

Arrival-angle determination unit 26 a detects a peak direction based onan arrival-angle evaluation result of arrival-angle evaluation unit 25 aevery Δθ in the variable range of θ, and uses the detected direction asan arrival-angle estimation value of the incident waves.

In the present embodiment, the array antenna having theconstant-interval linear array shape has been employed, and the realsteering vector has been derived by unitary matrix transformation. Thepositive-region arrival-angle evaluation value can be converted to thenegative-region arrival-angle evaluation value using vectors c1, c2calculated when the positive-region arrival-angle evaluation value arederived. The calculation amount in the arrival-angle evaluation can bereduced substantially in half compared with embodiment 1.

The present embodiment can be applied to embodiment 6 by a similarequation transformation.

11. Eleventh Exemplary Embodiment

FIG. 13 is a block diagram illustrating the other configuration ofdirection estimating processor 12 of the radio-wave arrival-directionestimating apparatus of the present invention. Components other than thedirection estimating processor in the radio-wave arrival-directionestimating apparatus are similar to those in embodiment 1 described inFIG. 1, so that diagrams and descriptions of these components areomitted. Components different from embodiment 1 will be mainly describedhereinafter.

The configuration in the present invention includes the followingcomponents, in addition to direction estimating processor 12 shown inFIG. 1:

high-accuracy arrival-angle evaluation unit 60 for calculating anevaluation value of an arrival-angle evaluation function at an angleinterval smaller than an angle interval calculated by an arrival-angleevaluation unit; and

high-accuracy arrival-angle determination unit 61 for highly accuratelydetermining an arrival angle based on the evaluation value byhigh-accuracy arrival-angle evaluation unit 60.

The following operations are similar to those in embodiment 1:

correlation matrix R is fed into direction estimating processor 12 k;

triangular matrix calculation unit 9 calculates triangular matrix L; and

arrival-angle determination unit 11 detects a peak direction based on anarrival-angle evaluation result of arrival-angle evaluation unit 10every Δθ in a variable range of θ, and uses the detected direction as anarrival-angle estimation value of the incident waves.

FIG. 14 is a graph illustrating operations of high-accuracyarrival-angle evaluation unit 60 and high-accuracy arrival-angledetermination unit 61. Arrival-angle evaluation unit 60 reevaluates karrival angles θk (k is a natural number) supplied from arrival-angledetermination unit 11 in angle range Wk of φ satisfying(θk−Δθ)<φ<(θ+Δθ), at angle step Δφ smaller than the angle step Δθ inarrival-angle evaluation unit 10, and using the arrival-angle evaluationfunction. Arrival-angle evaluation unit 60 then outputs the resultantarrival angle, which is highly accurate, to arrival-angle determinationunit 61.

Arrival-angle determination unit 61, based on evaluated values in kangle ranges Wk,.detects peak direction φpeak,k in each angle range Wk,and outputs the peak direction as an evaluated high-accuracy arrivalangle.

In the present embodiment, an arrival-angle has been more accuratelyreevaluated at a step smaller than angle step Δθ in arrival-angleevaluation unit 10 restrictively in a range around the arrival angleestimated in arrival-angle determination unit 11. Therefore, thedirection estimating processor in the present embodiment not onlyproduces the advantage shown in embodiment 1, but also can highlyaccurately estimate the arrival angle without unnecessarily increasingthe calculation amount for the arrival-angle evaluation function.

The operations in the present embodiment have been described in thestructure comprising high accuracy evaluation unit 60 and high-accuracyarrival-angle determination unit 61 in addition to direction estimatingprocessor 12 shown in embodiment 1. The present embodiment can produce asimilar advantage even in a structure comprising these units in additionto direction estimating processor shown in each of embodiments 2 to 10.

12. Twelfth Exemplary Embodiment

FIG. 15 is a block diagram illustrating a structure of a directivityvariable receiver of the present invention. The directivity variablereceiver in FIG. 15 selects a plurality of sector antennas withdifferent main beam directions, and changes the directivity, based onarrival-direction estimation result 64 derived by arrival-directionestimating apparatus 63 as described in embodiments 1 to 11. Operationsin arrival-direction estimating apparatus 63 are similar to thosedescribed above, so that descriptions of the operations are omitted.Additional components will be described hereinafter.

The directivity variable receiver comprises arrival-direction estimatingapparatus 63, m (≧2) sector antennas 65-1 to 65-m with different mainbeam directions, sector switch 66, sector control unit 67, and receivingunit 68.

Operations for estimating a radio-wave arrival direction using receivedsignals 2-1 to 2-M obtained by an array antenna are similar to thosedescribed in embodiments 1 to 11. Here the array antenna comprises aplurality of antenna elements 1—1 to 1-M. Final arrival-directionestimation result 64 is fed into sector control unit 67. Sector controlunit 67, based on estimation result 64, selects the ms-th sector antennahaving a main beam direction closest to the estimated direction from theplurality of sector antennas 65-1 to 65-m. Sector control unit 67further controls sector switch 66 based on sector control signal 69 toconnect sector switch 66 to receiving unit 68. Receiving unit 68demodulates signal 70 received by the ms-th sector antenna.

These operations allow the selection of the optimal sector antennahaving the main beam direction closest to the arrival direction from aplurality of sector antennas 65-1 to 65-m, and provide received signal70 with a high signal-to-noise ratio. Many waves having directionsdifferent from the main beam direction of the selected antenna can besuppressed, and interference between codes can be reduced.

The present embodiment shows a structure of the receiver; however, thereceiver can be also used as a transmitter by replacing receiving unit68 with a transmitting unit. In this case, transmitted power is reducedand radio waves are not radiated in unnecessary directions, so thatinterference with other station can be reduced.

Receiving unit 68 and transmitting unit 71 may be inter-coupled througha switch 72 as shown in FIG. 16 to provide a transceiver capable ofswitching between the reception and the transmission.

13. Thirteenth Exemplary Embodiment

FIG. 17 is a block diagram illustrating another structure of adirectivity variable receiver of the present invention. The directivityvariable receiver in FIG. 17 changes directivity and receives signals,based on arrival-direction estimation result 64 derived byarrival-direction estimating apparatus 63 as described in embodiments 1to 11. Operations in arrival-direction estimating apparatus 63 aresimilar to those described in embodiments 1 to 11, so that descriptionsof the operations are omitted. Additional components will be describedhereinafter.

L (>1) antenna elements 75-1 to 75-L may have a structure for dividingsignals sent from antenna elements 1—1 to 1-M in FIG. 1 into two, butantenna elements having a different structure will be describedhereinafter. Receiving units 77-1 to 77-L connected to respectiveantenna elements 75-1 to 75-L convert frequencies of signals 76-1 to76-L received by antenna elements 75-1 to 75-L, and then demodulate theconverted signals to signals 78-1 to 78-L comprising orthogonal I and Qsignals. A/D converters 79-1 to 79-L convert respective demodulatedsignals 78-1 to 78-L, which are analog, to complex digital signals 80-1to 80-L. Sampling frequencies fs of A/D converters 79-1 to 79-L mustsatisfy Nyquist condition, fs>2WB, in band WB (Hz) of transmittedmodulated wave so that the signals can be subsequently demodulated.Directivity control unit 81 assigns complex weights to complex digitalsignals 80-1 to 80-L, based on arrival-direction estimation result 64from arrival-direction estimating apparatus 63. Here the complex weightsare used for controlling the directivity. Receiving unit 68 receives theweighted signals.

As discussed above, directivity control unit 81 assigns complex weightsto complex digital signals 80-1 to 80-L and combines the signals witheach other to generate directivity in the direction of arrival-directionestimation result 64. A more optimal directivity pattern can be createdin this case, communication quality higher than that using a sectorantenna is allowed.

The present embodiment shows a structure for controlling the directivityin the receiver; however, a structure for controlling the directivity ina transmitter may be also employed as shown in FIG. 18. In this case,transmitted power is reduced and radio waves are not radiated inunnecessary directions, so that interference with other station can bereduced.

In FIG. 18, directivity control unit 83 receives signal 82 transmittedfrom transmitting unit 71. Directivity control unit 83 dividestransmitted signal 82 into L signals. Directivity control unit 83 thenassigns complex weights for controlling the directivity to respectivedivided signals 82, based on arrival-direction estimation result 64 fromarrival-direction estimating apparatus 63, and outputs resultant complexdigital signals 84-1 to 84-L. D/A converters 85-1 to 85-L convert thedigital signals to analog signals, and output the analog signals as baseband signals 86-1 to 86-L. Transmission frequency converters 87-1 to87-L convert frequencies of base band signals 86-1 to 86-L to atransmission frequency band, and output resultant RF signals 88-1 to88-L. Antenna elements 89-1 to 89-L transmit signals.

A transceiver having functions shown in FIG. 17 and FIG. 18 can beemployed. In this case, communication quality can be improved, andtransmitted power is reduced and radio waves are not radiated inunnecessary directions to reduce interference with other station.

The radio-wave arrival-direction estimating apparatus of the presentinvention can reduce a total calculation amount for arrival-angleevaluation using an arrival-angle evaluation function, without causingestimation accuracy degradation of the arrival direction. The estimatingapparatus can also speed a calculation process or simplify an apparatusstructure. Additionally, high quality communication is allowed, when thetransmitting units or the receiving units in the transceiver haveadditional antennas having a directivity control function for generatingdirectivity to the arriving direction of the arrival-directionestimating apparatus.

What is claimed is:
 1. A radio-wave arrival-direction estimatingapparatus comprising: an array antenna including a plurality of antennaelements; a receiving unit for converting frequency of a RF signalreceived by each of the antenna elements in said array antennaedemodulating the converted signal, and outputting the demodulatedsignal; an A/D converter tar converting the demodulated signal toecomplex digital signal; a correlation matrix calculation unit forcalculating a correlation matrix by correlation calculation at thecomplex digital signal between the antenna elements; a noise spatialeigenmatrix calculation unit for calculating a noise spatial eigenmatrixby eigenvalue factorization of the correlation matrix, one of a row anda column of the noise spatial eigenmatrix being an eigenvector belongingto a noise eigen-space; a triangular matrix calculation unit forfactorizing a matrix including a product of the noise spatialeigenmatrix and a conjugated and transposed matrix of the noise spatialeigenmatrix to a product of one of an upper triangular matrix and alower triangular matrix; an arrival-angle evaluation unit forcalculating an evaluation value of an arrival-angle evaluation functionevery predetermined angle, the arrival-angle evaluation function beingexpressed using the one of the upper triangular matrix and the lowertriangular matrix; and an arrival-angle determination unit fordetermining an arrival angle based on the evaluation value from saidarrival-angle evaluation unit.
 2. A radio-wave arrival-directionestimating apparatus according to claim 1 further comprising a unitarytransforming unit for unitary-transforming the correlation matrix,wherein the plurality of antenna elements are arranged linearly at aconstant interval, and said noise spatial eigenmatrix calculation unitapplies the eigenvalue factorization to the unitary-transformedcorrelation matrix.
 3. A radio-wave arrival-direction estimatingapparatus according to claim 1, wherein said triangular matrixcalculation unit factorizes in put matrix R to product U^(H)U of uppertriangular matrix U by cholesky factorization.
 4. A radio-wavearrival-direction estimating apparatus according to claim 1, whereinsaid triangular matrix calculation unit factorizes input matrix R toproduct LL^(H) of lower triangular matrix L by cholesky factorization.5. A radio-wave arrival-direction estimating apparatus according toclaim 1, wherein said triangular matrix calculation unit factorizes aninput matrix to product U^(H)DU of upper triangular matrix U anddiagonal matrix D by modified cholesky factorization.
 6. A radio-wavearrival-direction estimating apparatus according to claim 2, whereinsaid triangular matrix calculation unit factorizes an input matrix toproduct LDL^(H) lower triangular matrix L and diagonal matrix D bymodified cholesky factorization.
 7. A radio-wave arrival-directionestimating apparatus according to claim 1, wherein said correlationmatrix calculation unit calculates a correlation matrix, applies aspatial smoothing technique to the correlation matrix, and outputs aresultant matrix.
 8. A radio-wave arrival-direction estimating apparatusaccording to claim 1, wherein said array antenna includes a plurality ofantenna elements arranged linearly at a constant interval, and saidarrival-angle evaluation unit comprises a positive-region evaluationunit for calculating an evaluation value of an arrival-angle evaluationfunction for positive angle θ with reference to a bore-sight directionof said array antenna, and a negative-region evaluation unit forconverting the evaluation value by the positive-region evaluation unitto an arrival-angle evaluation value for negative angle (−θ).
 9. Aradio-wave arrival-direction estimating apparatus according to claim 1,wherein said array antenna has a linear array shape, and saidarrival-angle evaluation unit sets an angle interval in an end firedirection of said array antenna to be larger than an angle interval in abore-sight direction, and calculates an evaluation value of anarrival-angle evaluation function.
 10. A radio-wave arrival-directionestimating apparatus according to claim 1, further comprising: ahigh-accuracy arrival-angle evaluation unit for calculating anevaluation value of an arrival-angle evaluation function at an angleinterval smaller than an angle interval calculated by said arrival-angleevaluation unit, in a predetermined angle range around the arrival anglesupplied from said arrival-angle determination unit; and a high-accuracyarrival-angle determination unit for highly accurately determining anarrival angle based on the evaluation value by said high-accuracyarrival-angle evaluation unit.
 11. A radio-wave arrival-directionestimating apparatus comprising: an array antenna including a pluralityof antenna elements; an intermediate-frequency receiving unit forperforming frequency conversion and phase detection of a RF signalreceived by each of the antenna elements, and outputting an intermediatefrequency signal; an intermediate-frequency A/D converter for convertingthe intermediate frequency signal to an intermediate-frequency digitalsignal; a digital orthogonal wave detector for orthogonally demodulatingthe intermediate-frequency digital signal; a correlation matrixcalculation unit for calculating a correlation matrix by correlationcalculation or the complex digital signal between the antenna elements;a noise spatial eigenmatrix calculation unit for calculating a noisespatial eigenmatrix by eigenvalue factorization of the correlationmatrix, one of a row and a column of the noise spatial eigenmatrix beingan eigenvector belonging to a noise eigen-space; a triangular matrixcalculation unit for factorizing a matrix including a product of thenoise spatial eigenmatrix and a conjugated and transposed matrix of thenoise spatial eigenmatrix to a product of one of an upper triangularmatrix and a lower triangular matrix; an arrival-angle evaluation unitfor calculating an evaluation value of an arrival-angle evaluationfunction every predetermined angle, the arrival-angle evaluationfunction being expressed using the one of the upper triangular matrixand the lower triangular matrix, and an arrival-angle determination unitfor determining an arrival angle based on the evaluation value from saidarrival-angle evaluation unit.
 12. A radio-wave arrival-directionestimating apparatus comprising: an array antenna including a pluralityof antenna elements; a receiving unit for converting frequency of a RFsignal received by each of the antenna elements in said array antenna,demodulating the converted signal, and outputting the demodulatedsignal; an A/D converter for converting the demodulated signal to acomplex digital signal; a correlation matrix calculation unit tarcalculating a correlation matrix by correlation calculation of thecomplex digital signal between the antenna elements; an inverse matrixcalculating unit for calculating an inverse matrix of the correlationmatrix; a triangular matrix calculation unit tar factorizing the inversematrix to a product of one of an upper triangular matrix and a lowertriangular matrix, an arrival-angle evaluation unit for calculating anevaluation value of an arrival-angle evaluation function everypredetermined angle, the arrival-angle evaluation function beingexpressed using the one of the upper triangular matrix and the lowertriangular matrix; and an arrival-angle determination unit fordetermining an arrival angle based on the evaluation value from saidarrival-angle evaluation unit.
 13. A radio-wave arrival-directionestimating apparatus according to claim 12, further comprising a unitarytransforming unit for unitary-transforming the correlation matrix,wherein the plurality of antenna elements are arranged linearly at aconstant interval, and said inverse matrix calculation unit calculatesan inverse matrix of the unitary-transformed correlation matrix.
 14. Aradio-wave arrival-direction estimating apparatus, according to claim12, wherein said triangular matrix calculation unit factorizes inputmatrix R to product U^(H)U of upper triangular matrix U by choleskyfactorization.
 15. A radio-wave arrival-direction estimating apparatusaccording to claim 12, wherein said triangular matrix calculation unitfactorizes input matrix R to product LL^(H) of lower triangular matrix Lby cholesky factorization.
 16. A radio-wave arrival-direction estimatingapparatus according to claim 12, wherein said triangular matrixcalculation unit factorizes an input matrix to product U^(H)DU of uppertriangular matrix U and diagonal matrix D by modified choleskyfactorization.
 17. A radio-wave arrival-direction estimating apparatusaccording to claim 12, wherein said triangular matrix calculation unitfactorizes an input matrix to product LDL^(H) of lower triangular matrixL and diagonal matrix 0 by modified cholesky factorization.
 18. Aradio-wave arrival-direction estimating apparatus according to claim 12,wherein said correlation matrix calculation unit calculates acorrelation matrix, applies a spatial smoothing technique to thecorrelation matrix, and outputs a resultant matrix.
 19. A radio-wavearrival-direction estimating apparatus according to claim 12, whereinsaid array antenna includes a plurality of antenna elements arrangedlinearly at a constant interval, and said arrival-angle evaluation, unitcomprises a positive-region evaluation unit for calculating anevaluation value of an arrival-angle evaluation function for positiveangle θ with reference to a bore-sight direction of said array antenna,and a negative-region evaluation unit for converting the evaluationvalue by the positive-region evaluation unit to an arrival-angleevaluation value for negative angle (−θ).
 20. A radio-wavearrival-direction estimating apparatus according to claim 12, whereinsaid array antenna has a linear array shape, and said arrival-angleevaluation unit sets an angle interval in an end fire direction of saidarray antenna to be larger than an angle interval in a bore-sightdirection, and calculates an evaluation value of an arrival-angleevaluation function.
 21. A radio-wave arrival-direction estimatingapparatus according to claim 12, further comprising: a high-accuracyarrival-angle evaluation unit for calculating an evaluation value of anarrival-angle evaluation function at an angle interval smaller than anangle interval calculated by said arrival-angle evaluation unit, in apredetermined angle range around the arrival angle supplied from saidarrival-angle determination unit; and a high-accuracy arrivaldetermination unit for highly accurately determining an arrival anglebased on the evaluation value by said high-accuracy arrival-angleevaluation unit.
 22. A radio-way, arrival-direction estimating apparatuscomprising; an array antenna including a plurality of antenna elements;an intermediate-frequency receiving unit for performing frequencyconversion and phase detection of a RF signal received by each of theantenna elements, and outputting an intermediate frequency signal; anintermediate-frequency A/D converter for converting the intermediatefrequency signal to an intermediate-frequency digital signal; a digitalorthogonal wave detector for orthogonally demodulating theintermediate-frequency digital signal; a correlation matrix calculationunit for calculating a correlation matrix by correlation calculation ofthe complex digital signal between the antenna elements; an inversematrix calculation unit for calculating an inverse matrix of thecorrelation matrix; a triangular matrix calculation unit for factorizingthe inverse matrix to a product of one of an upper triangular matrix anda lower triangular matrix; an arrival-angle evaluation unit forcalculating an evaluation value of an arrival-angle evaluation functionevery predetermined angle, the arrival-angle evaluation function beingexpressed using the one of the upper triangular matrix and the lowertriangular matrix; and an arrival-angle determination unit fordetermining an arrival angle based on the evaluation value by saidarrival-angle evaluation unit.
 23. A radio-wave arrival-directionestimating apparatus comprising: an array antenna including a pluralityof antenna elements; a receiving unit for converting frequency of a RFsignal received by cacti at the antenna elements in said array antenna,demodulating the converted signal, and outputting the demodulatedsignal; an A/D converter for converting the demodulated signal to acomplex digital signal; a correlation matrix calculation unit forcalculating a correlation matrix by correlation calculation of thecomplex digital signal between the antenna elements; a triangular matrixcalculation unit for factorizing the correlation matrix to a product ofone of an upper triangular matrix and a lower triangular matrix; aninverse matrix calculation unit for calculating an inverse matrix of theone of the upper triangular matrix and the lower triangular matrix; anarrival-angle evaluation unit for calculating an evaluation value of anarrival-angle evaluation function every predetermined angle, thearrival-angle evaluation function being expressed using the inversematrix of the one of the upper triangular matrix and the lowertriangular matrix; and an arrival-angle determination unit fordetermining an arrival angle based on the evaluation value by saidarrival-angle evaluation unit.
 24. A radio-wave arrival-directionestimating apparatus according to claim 23 further comprising a unitarytransforming unit for unitary-transforming the correlation matrix,wherein the plurality of antenna elements are arranged linearly at aconstant interval, and said triangular matrix calculation unitfactorizes the unitary-transformed correlation matrix to a product ofone of an upper triangular matrix and a lower triangular matrix.
 25. Aradio-wave arrival-direction estimating apparatus according to claim 23,wherein said triangular matrix calculation unit factorizes input matrixR to product U^(H)U of upper triangular matrix U by choleskyfactorization.
 26. A radio-wave arrival-direction estimating apparatusaccording to claim 23, wherein said triangular matrix calculation unitfactorizes input matrix R to product LLH of lower triangular matrix L bycholesky factorization.
 27. A radio-wave arrival-direction estimatingapparatus according to claim 23, wherein said triangular matrixcalculation unit factorizes an input matrix to product U^(H)U of uppertriangular matrix U and diagonal matrix D by modified choleskyfactorization.
 28. A radio-wave arrival-direction estimating apparatusaccording to claim 23, wherein said triangular matrix calculation unitfactorizes an input matrix to product LDL^(H) of lower triangular matrixL and diagonal matrix D by modified cholesky factorization.
 29. Aradio-wave arrival-direction estimating apparatus according to claim 23,wherein said correlation matrix calculation unit calculates acorrelation matrix, applies a spatial smoothing technique to thecorrelation matrix, and outputs a resultant matrix.
 30. A radio-wavearrival-direction estimating apparatus according to claim 23, whereinsaid array antenna includes a plurality of antenna elements arrangedlinearly at a constant interval, and said arrival-angle evaluation unitcomprises a positive-region evaluation unit for calculating anevaluation value or an arrival-angle evaluation function for positiveangle θ with reference to a bore-sight direction of said array antenna,and a negative-region evaluation unit for converting the evaluationvalue by the positive-region evaluation unit to an arrival-angleevaluation value for negative angle (−θ).
 31. A radio-wavearrival-direction estimating apparatus according to claim 23, whereinsaid array antenna has a linear array shape, and said arrival-angleevaluation unit sets an angle interval in an end fire direction of saidarray antenna to be larger than an angle interval in a bore-sightdirection, and calculates an evaluation value of an arrival-angleevaluation function.
 32. A radio-wave arrival-direction estimatingapparatus according to claim 23, further comprising: a high-accuracyarrival-angle evaluation unit for calculating an evaluation value of anarrival-angle evaluation function at an angle interval smaller than anangle interval calculated by said arrival-angle evaluation unit, in apredetermined angle range around the arrival angle supplied from saidarrival-angle determination unit; and a high-accuracy arrival-angledetermination unit for highly accurately determining an arrival anglebased on the evaluation value by said high accuracy arrival-angleevaluation unit.
 33. A radio-wave arrival-direction estimating apparatuscomprising: an array antenna including a plurality of antenna elements;an intermediate-frequency receiving unit for performing frequencyconversion and phase detection of a RF signal received by each of theantenna elements, and outputting an intermediate frequency signal; anintermediate-frequency A/D converter for converting the intermediatefrequency signal to an intermediate-frequency digital signal; digitalorthogonal wave detector for orthogonally demodulating theintermediate-frequency digital signal; a correlation matrix calculationunit for calculating a correlation matrix by correlation calculation ofthe complex digital signal between the antenna elements; a triangularmatrix calculation unit for factorizing the correlation matrix to aproduct of one of an upper triangular matrix and a lower triangularmatrix; an inverse matrix calculation unit for calculating an inversematrix at the one of an upper triangular matrix and a lower triangularmatrix; an arrival-angle evaluation unit for calculating an evaluationvalue of an arrival-angle evaluation function every predetermined angle,the arrival-angle evaluation function being expressed using the inversematrix of the one of the upper triangular matrix and the lowertriangular matrix; and an arrival-angle determination unit fordetermining an arrival angle based on the evaluation value by saidarrival-angle evaluation unit.
 34. A radio-wave arrival-directionestimating apparatus comprising: an array antenna including a pluralityat antenna elements, a receiving unit for converting frequency of a RFsignal received by each of the antenna elements in said array antenna,demodulating the converted signal, and outputting the demodulatedsignal; an A/D converter far converting the demodulated signal to acomplex digital signal; a correlation matrix calculation unit forcalculating a correlation matrix by correlation calculation of thecomplex digital signal between the antenna elements; a triangular matrixcalculation unit for factorizing the correlation matrix to a product ofone of an upper triangular matrix and a lower triangular matrix; anarrival-angle evaluation unit for calculating an evaluation value of anarrival-angle evaluation function every predetermined angle, thearrival-angle evaluation function being expressed using the one of theupper triangular matrix and the lower triangular matrix; and anarrival-angle determination unit for determining an arrival angle basedon the evaluation value by said arrival-angle evaluation unit.
 35. Aradio-wave arrival-direction estimating apparatus according to claim 34further comprising a unitary transforming unit for unitary-transformingthe correlation matrix, wherein the plurality of antenna elements arearranged linearly at a constant interval, and said triangular matrixcalculation unit factorizes the unitary-transformed correlation matrixto a product of one of an upper triangular matrix and a lower triangularmatrix.
 36. A radio-wave arrival-direction estimating apparatusaccording to claim 34, wherein said triangular matrix calculation unitfactorizes input matrix R to product U^(H)U of upper triangular matrix Uby cholesky factorization.
 37. A radio-wave arrival-direction estimatingapparatus according to claim 34, wherein said triangular matrixcalculation unit factorizes input matrix R to product LL^(H) of lowertriangular matrix L by cholesky factorization.
 38. A radio-wavearrival-direction estimating apparatus according to claim 34, whereinsaid triangular matrix calculation unit factorizes an input matrix toproduct U^(H)U of upper triangular matrix U and diagonal matrix D bymodified cholesky factorization.
 39. A radio-wave arrival-directionestimating apparatus according to claim 34, wherein said triangularmatrix calculation unit factorizes an input matrix to product LDL^(H) oflower triangular matrix L and diagonal matrix D by modified choleskyfactorization.
 40. A radio-wave arrival-direction estimating apparatusaccording to claim 34, wherein said correlation matrix calculation unitcalculates a correlation matrix, applies a spatial smoothing techniqueto the correlation matrix, and outputs a resultant matrix.
 41. Aradio-wave arrival-direction estimating apparatus according to claim 34,wherein said array antenna includes a plurality of antenna elementsarranged linearly at a constant interval, and said arrival-angleevaluation unit comprises a positive-region evaluation unit forcalculating an evaluation value of an arrival-angle evaluation functionfor positive angle θ with reference to a bore-sight direction of saidarray antenna, and a negative-region evaluation unit far converting theevaluation value by the positive-region evaluation unit to anarrival-angle evaluation value for negative angle (−θ).
 42. A radio-wavearrival-direction estimating apparatus according to claim 34, whereinsaid array antenna has a linear array shape, and said arrival-angleevaluation unit sets an angle interval in an end fire direction of saidarray antenna to be larger than an angle interval in a bore-sightdirection, and calculates an evaluation value of an arrival-angleevaluation function.
 43. A radio-wave arrival-direction estimatingapparatus according to claim 34, further comprising a high-accuracyarrival-angle evaluation unit for calculating an evaluation value of anarrival-angle evaluation function at an angle interval smaller than anangle interval calculated by said arrival-angle evaluation unit, in apredetermined angle range around the arrival angle supplied from saidarrival-angle determination unit; and a high-accuracy arrival-angledetermination unit for highly accurately determining an arrival anglebased on the evaluation value by said high-accuracy arrival-angleevaluation unit.
 44. A radio-wave arrival-direction estimating apparatuscomprising: an array antenna including a plurality or antenna elements;an intermediate-frequency receiving unit for performing frequencyconversion and phase detection of a RF signal received by each of theantenna elements, and outputting an intermediate frequency signal; anintermediate-frequency A/D converter for converting the intermediatefrequency signal to an intermediate-frequency digital signal; a digitalorthogonal wave detector tar orthogonally demodulating theintermediate-frequency digital signal; a correlation matrix calculationunit for calculating a correlation matrix by correlation calculation ofthe complex digital signal between the antenna elements; a triangularmatrix calculation unit for factoring the correlation matrix to aproduct of one of an upper triangular matrix and a lower triangularmatrix; an arrival-angle evaluation unit for calculating an evaluationvalue of an arrival-angle evaluation function every predetermined angle,the arrival-angle evaluation function being expressed using the one ofthe upper triangular matrix and the lower triangular matrix; and anarrival-angle determination unit for determining an arrival angle basedon the evaluation value by said arrival-angle evaluation unit.
 45. Aradio-wave arrival-direction estimating apparatus comprising an arrayantenna including a plurality of antenna elements; a receiving unit forconverting frequency of a RF signal received by each of the antennaelements in said array antenna, demodulating the converted signal, andoutputting the demodulated signal; an A/D converter for converting thedemodulated signal to a complex digital signal; a correlation vectorcalculation unit for calculating a correlation vector by correlationcalculation between a reference antenna element and another antennaelement, the reference antenna element corresponding to a selectedcomplex digital signal; an arrival-angle evaluation unit for calculatingan evaluation value of an arrival-angle evaluation function everypredetermined angle, the arrival-angle evaluation function beingexpressed using the correlation vector; and an arrival-angledetermination unit for determining an arrival angle based on theevaluation value by said arrival-angle evaluation unit.
 46. A radio-wavearrival-direction estimating apparatus according to claim 45 furthercomprising a unitary transforming unit for unitary-transforming thecorrelation vector, wherein the plurality of antenna elements arearranged linearly at a constant interval, and said arrival-angleevaluation unit calculates an evaluation value of an arrival-angleevaluation function every predetermined angle, the arrival-angleevaluation function being expressed using the unitary-transformedcorrelation vector.
 47. A radio-wave arrival-direction estimatingapparatus according to claim 45, wherein said array antenna includes aplurality of antenna elements arranged linearly at a constant interval,and said arrival-angle evaluation unit comprises a positive-regionevaluation unit for calculating an evaluation value of an arrival-angleevaluation function for positive angle B with reference to a bore sightdirection of said array antenna, and a negative-region evaluation unitfor converting the evaluation value by the positive-region evaluationunit to an arrival-angle evaluation value for negative angle (−θ).
 48. Aradio-wave arrival-direction estimating apparatus according to claim 45,wherein said array antenna has a linear array shape, and saidarrival-angle evaluation unit sets an angle interval in an end firedirection of said array antenna to be larger than an angle interval in abore-sight direction, and calculates an evaluation value of anarrival-angle evaluation function.
 49. A radio-wave arrival-directionestimating apparatus according to claim 45, further comprising: ahigh-accuracy arrival-angle evaluation unit for calculating anevaluation value of an arrival-angle evaluating function at an angleinterval smaller than an angle interval calculated by said arrival-angleevaluation unit, in a predetermined angle range around the arrival anglesupplied from said arrival-angle determination unit; and a high-accuracyarrival-angle determination unit for highly accurately determining anarrival angle based on the evaluation value by said high-accuracyarrival-angle evaluation unit.
 50. A radio-wave arrival-directionestimating apparatus comprising: an array antenna including a pluralityat antenna elements; an intermediate-frequency receiving unit forperforming frequency conversion and phase detection of a RF signalreceived by each of the antenna elements, and outputting an intermediatefrequency signal; an intermediate-frequency A/D converter for convertingthe intermediate frequency signal to an intermediate-frequency digitalsignal; a digital orthogonal wave detector for orthogonally demodulatingthe intermediate-frequency digital signal; a correlation vectorcalculation unit for calculating a correlation vector by correlationcalculation between a reference antenna element and another antennaelement, the reference antenna element corresponding to a selectedcomplex digital signal; an arrival-angle evaluation unit for calculatingan evaluation value of an arrival-angle evaluation function everypredetermined angle, the arrival-angle evaluation function beingexpressed using the correlation vector; and an arrival-angledetermination unit for determining an arrival angle based on theevaluation value by said arrival-angle evaluation unit.